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Current Question (ID: 19622)

Question:

$\text{An external pressure } P \text{ is applied on a cube at } 0^\circ C \text{ so that it is equally compressed from all sides. } K \text{ is the bulk modulus of the material of the cube and } \alpha \text{ is its coefficient of linear expansion.}$ $\text{Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:}$

Options:

1. $\frac{P}{3 \alpha K}$
2. $\frac{P}{\alpha K}$
3. $\frac{3 \alpha}{P K}$
4. $3 P K \alpha$

Solution:

$\text{Hint: } B = \frac{-P}{\frac{dV}{V}}$ $B = \frac{-P}{\frac{dV}{V}}$ $\frac{dV}{V} = \frac{-P}{B}$ $dV = \frac{-PV}{B}$ $\text{By heating we have to increase the volume by } \frac{PV}{B}$ $\Delta V = V_\gamma \Delta T = V \times 3 \alpha \Delta T$ $V \times 3 \alpha \Delta T = \frac{PV}{B}$ $\Delta T = \frac{P}{3 \alpha B}$ $\text{Here } B = K$ $\therefore \Delta T = \frac{P}{3 \alpha K}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}